Math Problem Statement

Complete the table by calculating the missing values of x, x^2, and x^3.

Solution

To help you fill out this table, we need to calculate the values of x2x^2 and x3x^3 for different values of xx. Here's how we can proceed based on the numbers available in the image:

Given Data:

The numbers available for xx are: 0,5,10,50,1000, 5, 10, 50, 100

The corresponding squares x2x^2 and cubes x3x^3 will be:

  1. x=0x = 0:

    • x2=02=0x^2 = 0^2 = 0
    • x3=03=0x^3 = 0^3 = 0
  2. x=5x = 5:

    • x2=52=25x^2 = 5^2 = 25
    • x3=53=125x^3 = 5^3 = 125 (already filled in the table)
  3. x=10x = 10:

    • x2=102=100x^2 = 10^2 = 100
    • x3=103=1,000x^3 = 10^3 = 1,000 (already filled in the table)
  4. x=50x = 50:

    • x2=502=2,500x^2 = 50^2 = 2,500
    • x3=503=125,000x^3 = 50^3 = 125,000
  5. x=100x = 100:

    • x2=1002=10,000x^2 = 100^2 = 10,000
    • x3=1003=1,000,000x^3 = 100^3 = 1,000,000

Filling the Table:

Based on these calculations, the completed table should look like this:

xxx2x^2x3x^3
000
525125
101001,000
502,500125,000
10010,0001,000,000

Let me know if you have any questions or need further clarifications!

Here are 5 related questions:

  1. What is the relationship between the values of x2x^2 and x3x^3?
  2. How would you calculate x4x^4 for each xx in the table?
  3. If x=200x = 200, what would be x2x^2 and x3x^3?
  4. What happens to x2x^2 and x3x^3 as xx increases?
  5. How does x3x^3 grow in comparison to x2x^2?

Tip: When squaring or cubing numbers, always remember that even small increases in xx lead to much larger increases in x2x^2 and x3x^3.

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Math Problem Analysis

Mathematical Concepts

Exponents
Squares and Cubes

Formulas

x^2 (square of x)
x^3 (cube of x)

Theorems

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Suitable Grade Level

Grades 6-8